The Belgian teenager picked up the knock during a training session at Cobham on Thursday.
Lavia, who was signed by Chelsea under the noses of Liverpool this summer in a deal worth up to £58million, is yet to make his debut for the Blues having arrived lacking match fitness.
It is another blow for manager Mauricio Pochettino, who has endured a string of injuries to players since his appointment at the beginning of the summer.
Captain Reece James continues to be plagued by setbacks, having been sidelined with another hamstring injury, and joins Wesley Fofana - ruled out for most of the season with a knee injury - and Christopher Nkunku - due back at the end of the year after picking up a knee complaint during pre-season - on the treatment table.
Carney Chukwuemeka is set for another month on the sidelines after damaging his knee during last month’s 3-1 defeat to West Ham, in which he scored Chelsea’s only goal of the game.
In more positive news, Trevoh Chalobah and Benoit Badiashile are nearing returns and Armando Broja is building up his fitness after missing the second half of last season.